Signal processing apparatus

ABSTRACT

Disclosed herein are methods and apparatus for analyzing signals containing phase information and for deriving therefrom digital representations of that phase information. The phase information may be present in resolver-type signals or may be contained in AC signals having a phase relative to a reference. In both cases the phase sensitive information is converted to DC signals proportional to sin theta and cos theta . In one embodiment a signal proportional to sin theta / theta is synthesized from the signals proportional to sin theta and cos theta . A signal proportional to sin theta is then integrated for a time t1 after which a negative signal proportional to sin theta / theta is integrated for a time t2 until the integrator output returns to its original state. Counting during t2 results in a count directly proportional to theta . In another embodiment a signal proportional to sin theta is integrated during t1 and a negative signal proportional to cos theta is integrated during t2. This results in a count directly proportional to tan theta . A look-up table then provides the conversion from tan theta to theta .

United States Patent 1 1 Reichnebacher 1 Oct. 1,1974

1 SIGNAL PROCESSING APPARATUS [75] Inventor: George Reichnebacher, Stony Brook, NY.

[22] Filed: Mar. 23, 1973 [21] Appl. No.: 344,112

[52] US. Cl. 340/347 SY, 340/347 NT [51] Int. Cl. [103k 13/20 [58] Field of Search. 340/347 SY, 347 NT, 347 AD [56] References Cited UNITED STATES PATENTS 3,277,461 4/1966 Selvin 340/347 SY 3,295,125 12/1966 Idelsohn et a1. 340/347 SY 3,316,547 4/1967 Ammann... 340/347 NT 3,504,361 3/1970 Catton 340/347 SY 3,510,867 5/1970 Sliwa 340/347 SY 3,516,084 6/1970 Sacks et al 340/347 SY 3,618,073 11/1971 Domch'ick et a1. 340/347 SY 3,710,374 1/1973 Kelly 340/347 NT 3,713,141 1/1973 Higgins et a1. 340/347 SY OTHER PUBLICATIONS Crider et al. IBM Technical Disclosure Bulletin Vol. 12 No. 10, March, 1970, pg. 1,602

Primary ExaminerCharles D. Miller Attorney, Agent, or Firm-Morgan, Finnegan, Durham & Pine [57] ABSTRACT Disclosed herein are methods and apparatus for ana lyzing signals containing phase information and for deriving therefrom digital representations of that phase information. The phase information may be present in resolver-type signals or may be contained in AC signals having a phase relative to a reference. In both cases the phase sensitive information is converted to DC signals proportional to sim) and c050. In one embodiment a signal proportional to sin6/6 is synthesized from the signals proportional to S1110 and cosO. A signal proportional to sinO is then integrated for a time t, after which a negative signal proportional to sin6/0 is integrated for a time t until the integrator output returns to its original state. Counting during results in a count directly proportional to 0. In another embodiment a signal proportional to sin() is integrated during t and a negative signal proportional to c056 is integrated during This results in a count directly proportional to tam). A look-up table then provides the conversion from tanO to 0.

18 Claims, 6 Drawing Figures i u W w w .1 1 l +8114 9 i I 25 27 I I 34 I 27. 33 i I U L i I I cmr I I 5 I is I Z3 1 l SING 36 I I i e A 1 I 1 1 l 24 I 1 s7 -3 I i 11 39,. l m J FF Dezscme 9 Comma? /%6SC7' Q5857 w C Al /Dow QwmL p 40 Fswow- BACKGROUND AND BRIEF DESCRIPTION OF THE INVENTION The invention disclosed herein relates to techniques and apparatus for analyzing signals containing phase information and for deriving therefrom digital repre sentations of that information.

Phase information is embodied in signals of various types. For example, phase information is contained in resolver-type signals of the form E sinfl sinwt and E cos sinwt. Phase information is also present in AC electrical signals of the form E,sin(wt+0), where 6 is the phase relative to a reference. It is often desirableto derive a digital representation of 0 from both types of signals, either for display or for subsequent processing. The instant invention teaches various ways in which this may be accomplished.

In one embodiment of the invention an AC signal of the form E,,sin(wt+0) is analyzed to derive therefrom DC voltages proportional to the quadrature and inphase components, i.e., sin0 and cos0. A signal proportional to sin0/6 is then synthesized from the signals proportional to sin0 and cos0. A signal proportional to sin0 is integrated for a time t, following which a negative signal proportional to sine/0 is integrated for a time t until the integrator output returns to its original state. Counting during t results in a count directly proportionalto 6, i.e., 6 t /t The technique for integrating one signal in one direction after which a second signal is integrated in the opposite direction is sometimes referred to as dual slope integration. Various techniques for carrying out dual slope integration are set forth in US. Pat. Nos. 3,051,939 and 3,316,547.

In a second embodiment of the invention a signal proportional to sin0 is integrated for a time I, after which a negative signal proportional to cos0 is integrated for a time 1 until the integrator output returns to its original state. Counting during t results in a count directly proportional to tan0, i.e., tan0 t /t,. A lookup table or other suitable means is used to provide a digital representation of 0 in accordance with the equation 0 tan t /t,.

Other objectives and advantages of the invention will be set forth in part hereafter and in part will be obvious herefrom or may be learned by practice with the invention, the same being realized and attained by means of the instrumentalities, combinations and improvements herein shown, described and claimed.

BRIEF DESCRIPTION OF THE DRAWINGS Serving to illustrate exemplary embodiments of the invention are the drawings, of-which:

FIG. I is a schematic diagram illustrating one manner in which in-phase and quadrature components may be derived; v

FIG. 2 is a timing diagram;

FIG. 3 is a schematic diagram illustrating one manner in which the phase angle 0 may be measured and digitized; I

FIG. 4 is a schematic diagram illustrating one manner in which voltages may be combined prior to integration; and

FIG. 5 is a schematic diagram illustrating the conversion of resolver-type signals from AC to DC.

DETAILED DESCRIPTION The invention will now be described in detail with reference to the drawings forming a part of this specification. In one embodiment of the invention the phase angle of an AC signal of the form E,sin(wt+0) is measured and digitized. This AC signal may be viewed as being composed of the fundamental component plus all higher harmonics plus noise. FIG. 1 is a schematic diagram illustrating the'manner in which the in-phase and quadrature components of the fundamental are derived.

As shown in FIG. '1, a reference signal E sin wt is applied to input filter 2, which is a two-pole low-pass filter. In the preferredembodiment, the reference signal has a constant amplitude which is achieved using conventional automatic gain control techniques. The output of filter-12 comprises the fundamental E sin wt and may also contain some higher order harmonics and noise. This output signal is fed to a phase locked loop comprising demodulator 3, filter 4, VCO 5 and waveform generator 6. Demodulator 3 is a full-wave phase sensitive demodulator or multiplier of conventional design. Filter 4 is an active low pass filter and integrator which compensates the phase locked loop. VCO 5 is a narrow band, e.g., 37%, voltage controlled oscillator which may utilize unijunction transistors. The output frequency of VCO 5 is 12 times the input frequency. Waveform generator'fi comprises a counter and logic to generate two chopping waveforms which have 0 and phase shift with respect to the reference signal. The 90 chopping waveform is used to drive demodulator 3 which closes the phase locked loop. Demodulator 3 produces zero DC output when the phase locked loop is locked onto the reference signal.

In some applications it is advantageous to be able to phase shift the reference in a controlled manner. This is implemented by voltage source 1, potentiometer 7 and switch 8. With switch 8 in the OFFSET position, a variable offset DC signal is summed with the output of demodulator 3. The closed loop action is such as to maintain zero error signal into filter 4. It will do this by phase shifting the chopping signal with respect to the reference. The circuit shown in FIG. 1 allows for a i 45 phase shift.

FIG. 2 is a timing diagram for waveform generator 6. As previously noted, the VCO output is a train of pulses at 12 times the frequency of the reference signal. This output signal is counted down by a divide-by-IZ counter contained in waveform generator 6. The counter outputs,shown as A, B, C and D in FIG. 2, are combined to develop the 17/6 chopping waveforms also shown in FIG. 2.

Using a phase locked loop to derive the chopping waveforms has several distinct advantages. In the first place, the orthogonality of the 0 and 90 chopping waveforms is determined digitally instead of using conventional analog phase shifting techniques. This ensures a much greater accuracy over the input bandwidth. Secondly, 1r/6 chopping waveforms may be utilized which do not contain third or even order harmonics. Thus, to the extent the reference signal contains even and third harmonics, these will be rejected by demodulator 3. This choice of 17/6 chopping waveforms also meansthat the input filters may be considerably simpler than would otherwise be necessary and the problem of matching the phase shift and phase shift gradient with frequency of the input filters is minimized.

The signal whose phase is sought to be measured, i.e., E sin(wt+6), is applied to input filter 9, which is a twopole low-pass filter having substantially the same phase shift as input filter 2. The output of filter 9 is applied to phase sensitive demodulators 10 and 11 which are driven by the and 90 outputs from waveform generator 6. The outputs from demodulators and 11 are fed to low pass filters 12 and 13 respectively, which are three-pole Bessel active filters which suppress the extraneous AC demodulator outputs. The output of filter 12 is proportional to the in-phase component of the applied signal, i.e., cosO, while the output of filter 13 is proportional to the quadrature component, i.e., sin6. For purposes of convenience the proportionality factor is not expressed.

Referring to FIG. 3A the manner in which the signals proportional to sin6 and cos0 are manipulated to derive the phase angle 0 will now be explained. The signal proportional to c056 is fed to absolute value and polarity detector 14, which comprises a non-linear and a linear amplifier. The output of the polarity detector, which is a logic 1 when c056 is positive and logic 0 when cos0 is negative, is supplied to input C of decoder logic 15.

The signal proportional to sin0 is supplied to absolute value and polarity detector 16, which may also comprise a linear and a non-linear amplifier. The output of polarity detector 16, which is a logic 1 when sinB is positive and a logic 0 when sin6 is negative, is supplied to the S input of decoder logic 15. Absolute value and polarity detectors l4 and 16 contain a slight amount of hysteresis to prevent chatter.

Absolute value and polarity detectors 14 and 16 produce, respectively, outputs proportional to the absolute value of cost? and sin0. These two signals form the inputs to octant detector 17, which may comprise an operational amplifier containing a slight hysteresis. The output of octant detector 17, which is a logic 1 when cost? is greater than sin6 and a logic 0 when sin6 is greater than cost), is supplied to the OD input of decoder logic 15.

Octant sensing and switching is.employed to simplify the circuitry required by taking advantage of the fact that, within a quadrant, the sine and cosine are complementary functions i.e., cosO =sin(900). By breaking each quadrant up into octants the circuitry required is even further simplified, as will become apparent from the subsequent description of the system.

Decoder logic 15 operates upon the C, S and OD inputs to determine the octant in which 0 resides. Decoder logic 15 then controls switch 18 to effect polarity reversal of the cosine and sine absolute values produced by absolute value and polarity detectors l4 and 16 respectively. In addition, decoder logic 15 both presets and controls the direction of counting of counter/- processor 19. For example, if 6 were 10 then switch 18 would be in position A, counter/processor 19 would be preset to 0 and the direction of counting would be up. Similarly, if 0 were 80 switch 18 would be in position B, counter/processor 19 would be present to 90 and the direction of counting would be down. The octant switching, counter preset and direction of counting are set forth for each octant in TABLE 1, infra.

In order to determine the phase angle 0, two trigonometric functions are utilized. In one embodiment they are sine and sin6/0 A signal proportional to sin0 is readily available from absolute value and polarity detector 16 and is supplied by way of switch 18. The function sin0/6 must, however, be synthesized. The technique for doing so utilizes piecewise approximations over three segments comprising an octant. Thus, for example, the octant 045 is broken up into the segments -23.3, 23.3-35.2 and 35.2-45. Segment sensing and switching is effected by segment detectors 20 and 21, the inputs of which are the signals proportional to the absolute values of sin6 and C050 supplied by switch 18.

The negative function sin0/6 is synthesized by summing a portion of the signal proportional to sin6 with a portion of the signal proportional to c050. The following empirical equations approximate the function Ksin6/0 over the three segments comprising the octant.

(0 23.3); Ksin0/0 z 0.8528916 cos0+ 1.1665534 sin0 (23.3 352); Ksin0/0 0.286243 sin0 (35.2 45); Ksin9/0 0.741107 cost) 0.370758 sin0 0.8007726 cos0 TABLE 1 OCTANT SWITCHING SWITCH COUNTER Each of the above equations includes a scale factor of 0.872665 which is subsequently used in converting 0 from radians to degrees. The above equations also include a 01 zero offset bias which is taken out digitally later.

Referring now to FIG. 3B, segment detectors 20 and 21 comprise operational amplifiers which switch respectively at 233 and 35.2". At 23.3 sin6 0.3956, c050 0.9185 and tan0 0.4307. Thus, at 233 the signal at input A of segment detector 20 is 0.3956 volts, while the signal at input B is 0.9185 volts. In order to have segment detector 20 switch at 233, the cost) signal is attenuated by a factor of 0.4307, i.e., tan 23.3".

At 35.2 sin6 0.5764, cost) 0.8171 and tan!) 0.7054. Thus, at 352 the signal at input A of segment detector-21 is 0.5764 volts while the signal at input B is 0.8171 volts. In order to have segment detector 21 switch at 352, the cost) signal is attenuated by the factor 0.7054, i.e., tan 352. Although not shown in FIG. 4, both segment detectors 20 and 21 contain a slight hysterisis to prevent chatter at the threshold switching levels.

During the segment 0 233 both switches 22 and 23 are open. During the segment 23.3 35.2 switch 22 is open and switch 23 is closed. During the segment 35.2 45 both switches 22 and 23 are closed. The switching for each of the 24 segments is set forth in TABLE 2, infra.

TABLE 2 SEGMENT SWITCHING SEGMENT SWITCH l8 SWITCH 22 SWITCH 23 WGJU7UJWUU WCOUJWUJUJ OOUQOOOOQQOOOOQQOOOOOQ OQQGQOOOQOQOOQOOQOOQGQGO resistors 26 and 29 are added to the circuit by switch 23. Finally, during the segment 35.245 resistors and 28 are also added to the circuit by switch 22. Both relative and typical values for resistors 24 through 30 are set forth in TABLE 3, infra.-

Sin0 and Ksin0/6 are now processed to yield the desired information, i.e., 6. Clock 39 supplies clock pulses to counter/processor 19 which is preset by decoder logic 15 in accordance with the particular octant in which 0 resides. Counter/processor 19 controls FF 37 which in turn controls switches 32 and 38. Switch 32 is closed by FF 37 during the time t, which corresponds, for example, to 10,000 clock pulses. During the period 1 sinl9 is applied by switch 32 to the integrator comprising resistor 33, capacitor 34 and operational amplifier 35.. At the end of t, counter/processor 19 causes FF 37 to change state, thereby opening switch 32 and closing switch 38.

During the time period t Ksin6/0 is integrated until the output of the integrator returns to its original state, at which point zero crossing detector 36 supplies a reset signal to FF 37 and counter/processor l9. Integrating sin0 and l(sin6/6 in the manner just described establishes the following equations:

sin I. 6

sin 6t =K 0 and TABLE 3 TYPICAL RESISTOR VALUE TABLE 3-Continued RESISTOR VALUES Thus, the count registered by counter/processor 19 during time t is directly proportional to the desired angle 6 and is a digital representation thereof.

If, for example, 0 is 10 then counter/processor 19 will have been preset to 0 and, during the period t will countup to 10.03. The contents of counter/processor 19 will then be displayed digitally by readout 40. In order to convert 0 from radians to degrees, two scale factors are employed. The manner in which this is accomplished may be easily understood by means of the following example.

If 0 45 0.7854 radians, then sin0 0.7071 volts and sin0/0==0.90031 volts. Substituting these values in the above identity yields:

1 0.7071/0.90031 (10,000) 7,854 pulses. The desired'number of pulses, however, is 450 to produce a reading of 45.0", full scale being 360.0. To convert the 7,854 pulses to 450 pulses it is necessary to divide by a factor of 17.4533. To accomplish this, during the time period the output of clock 39 is divided by a factor of 20, which results in a count of 392.7 pulses for 6 45.0. To convert this number to 450 requires division by a factor of 0.872665. But this is precisely the scale factor previously introduced in connection with the piecewise approximations for synthesizing sin0/6. In this manner, the phase angle 0 in degrees is ascertained and displayed digitally by readout 40.

In accordance with the present invention it is also possible to integrate the signal proportional to sin0/6 for a time t after which the signal sin0 is integrated in the opposite direction for a time t until the integrator output returns to its original state. This results in the sin following equations:

' fr 6 M K I dr=j 0 0 0 Thus, the desired angle 0 is inversely proportional to the count registered by counter/processor 19 during the period 1 A simple manipulation by counter/- processor 19 is all that is required to convert 0 to a form suitable for display by readout 40.

Ii (2 cos J cos 0dr=KI 0 dr:

K cos 6) cos (it, t d 0 an Ktg The result is identical. This follows from the'fact that cost) sin(906). For purposes of this embodiment of the invention, therefore, using signals proportional to c050 and cos6/0 is the same as using signals proportional to sin0 and sin0/0. The results obtained in each case are identical.

In the practice of this invention it is also possible to utilize a signal proportional to the combination of sin6 and sin0/0 and a signal proportional to either sin0 or sin0/6. For example, integrating a signal proportional to sin0 for a time [1 and integrating a signal proportional to sin6 sine/0 in the opposite direction for a time t until the integrator output returns to its original state yields the following equation:

and

Thus, 6 is once again given in terms of t and t Simple manipulation by counter/processor 19 will place 6 in a form suitable for display by readout 40. For example, an up/down counter may be employed to count up during and count down during t to calculate t A second counter could then be employed to count up during 1 The ratio of these counter readings yields 6.

FIG. 4A illustrates one way in which the signals proportional to sin6 and sin6/0 may be combined. The signal proportional to sim) is supplied to switch 45 and to one input ofthe summing amplifier formed by resistors 41, 42 and 43 and operational amplifier 44. The signal proportional to sin6/6 is also fed to switch 45 and to the second input of the summing amplifier. The summing amplifier produces as an output a signal proportional to the combination of sin() and sin6/0. This output signal is also fed to switch 45. During the time t switch 45 selects one of the three input signals and applies it to switch 32 which is connected to the integrator during that time. During time switch 45 selects a different input signal and applies it to switch 38 which is connected to the integrator during that time.

In another embodiment of the invention it is not necessary to synthesize functions proportional to sin0/0 or cos0/6. Rather a signal proportional to sin0 is integrated during the time 1 and a signal proportional to cost) is integrated in the opposite direction during the time t which is required for the integrator to return to its original state. This establishes the following equations:

sin 6n cos 0t and tan 6=f2/t1.

Thus, the count accumulated in counter/processor 19 during the time t is directly proportional to a function cos 6t =sin Or Cot 6=t2/t1.

Once again, the count in counter/processor accumulated during t is directly proportional to a function of 0. Taking the inverse of that function yields the angle 0 which may be displayed by readout 40.

As with the signals proportional to sinO and sin6/0, it is also possible to use signals proportional to the combination of sin6 and cos0. To illustrate:

(2 sin 007 (sin 0 +cos 0)a't:

sin 6(t, t )=cos 0t and tan 0 The function of 0 is once again given in terms of I, and 1 A simple manipulation by counter/processor 19 will permit the inverse function to be obtained and displayed.

FIG. 4B shows one way in which the signals proportional to sin0 and cos() may be combined. Each of the circuit elements in FIG. 4B bears the same numerical designation and performs the same way as described in connection with FIG. 4A.

As noted previously, resolver-type signals also carry phase information. These signals are of the form E sin6 sinwt and E cos sinwt. The phase information may be separated from the AC carrier by any one of a number of known methods for AC/DC conversion. Rectification is but one example. AC/DC conversion yields DC signals proportional to sin6 and cos0. This conversion process is illustrated in FIG. 5. The DC signals proportional to sin0 and cos6 may now be manipulated in any one of the number of ways disclosed earlier to derive and display the phase information.

The invention disclosed and claimed herein is not limited to the specific mechanisms and techniques herein shown and described since modifications will undoubtedly occur to those skilled in the art. Hence, departures may be made from the form of the instant invention without departing from the principles thereof.

What is claimed is:

1. Signal processing apparatus for deriving a digital representation of 6 from signals proportional to sinO and cos0 including:

a. synthesizing means responsive to said signals proportional to sinO and cost) for deriving therefrom a signal proportional to sine/0;

b. integrating means operably connected to said synthesizing means and responsive to said signals proportional to sin!) and sin0/6 for integrating one of said signals in one direction for a time t and the other of said signals in the opposite direction for a time t -until the output of said integrating means returns to its original state; and

c. counting/processing means operably connected to said integrating means and responsive thereto for deriving therefrom a digital representation of 6.

2. Apparatus according to claim 1 wherein said signals proportional to sin6 and cos are derived from resolver-type signals proportional to sin6 sinwt and cos6 sinwt.

3. Signal processing apparatus for deriving a digital representation of 0 from signals proportional to sin0 and cost? including:

a. synthesizing means responsive to said signals proportional to sin!) and c050 for deriving therefrom an output signal proportional to sinO/O;

b. summing means operably connected to said synthesizing means and responsive to said signals proportional to sin!) and sin6/6 for developing therefrom a composite signal proportional to sin0 and sin0/0;

c. switching means operably connected to said synthesizing means and responsive to said signals proportional to sin0 and sin6/0 for selecting one of said signals;

d. integrating means operably connected to said summing means and said switching means and responsive to said selected signal and said composite signal for integrating one of said signals in one direction for a time I. and the other of said signals in the opposite direction for a time until the output of said integrating means returns to its original state; and

e. counting/processing means operably connected to said integrating means and responsive thereto for deriving therefrom a digital representation of 0.

4. Signal processing apparatus for deriving a digital representation of 0 from a signal proportional to sin(wt 0) and a reference signal including:

a. synthesizing means responsive to said signal proportional to sin(wt 0) and said reference signal for deriving therefrom signals proportional to sin() and sin0/6;

b. integrating means operably connected to said synthesizing means and responsive to said signals proportional to sin6 and sin0/6 for integrating one of said signals in one direction for a time t and the other of said signals in the opposite direction for a time r until the output of said integrating means returns to its original state; and

c. counting/processing means operably connected to said integrating means and responsive thereto for deriving therefrom a digital representation of 6.

5. Apparatus according to claim 4 further including display means operably connected to said counting/- processing means and responsive thereto for digitally displaying 0 in degrees.

6. Apparatus according to claim 4 wherein said synthesizing means includes means for deriving from said signal proportional to sin(wt+6) signals proportional to sin0 and c050 and means for synthesizing therefrom said signal proportional to sin6/0.

7. Apparatus according to claim 6 wherein said means for synthesizing said signal proportional to sin0/0 includes piecewise approximation means.

8. Apparatus according to claim 4 wherein said synthesizing means includes means for incorporating a scale factor into at least one of said signals proportional to sin0 and sinO/O for facilitating the conversion of 6 from radians to degrees.

9. Signal processing apparatus for deriving a digital representation of a 0 from a signal proportional to sin(wt-F0) and a reference signal including:

a. synthesizing means responsive to said signal proportional to sin(wt+6) and said reference signal for deriving therefrom signals proportional to sinB and sine/6;

b. integrating means operably connected to said synthesizing means and responsive thereto for integrating said signal proportional to sin!) in one direction for a time t and said signal proportional to sinO/O inthe opposite direction for a time t until said integrating means returns to its original state; and

c. counting means operably connected to said integrating means and. responsive thereto for counting during said time period t to generate a digital representation directly proportional to 6.

10. Apparatus according to claim 9 wherein said synthesizing means includes. means for incorporating a scale factor intov at least one of said signals proportional to sin6 and sin6/0'for facilitating the conversion of 0 from radians to degrees.

11. Apparatus according to claim 9 wherein said synthesizing means includes means for deriving said signal proportional to sin6/0 over an octant and further includes switching means for utilizing said signal proportional to sin6/0 over all eight octants.

12. Apparatus according to claim 11 wherein said synthesizing means includes segment sensing and switching means for deriving a piecewise approximation of said signalproportionalto sin6/6 over an octant.

13. Apparatus according to claim 12 wherein said segment sensing and. switching means effects said piecewise approximationsof said signal proportional to sin0/0 over three segments comprising an octant and wherein said segments comprise on the order of 23, 12 and 10.

14. Apparatus according to claim 11 wherein said switching means includes octant sensing and switching means for presetting said counting means and for controlling the direction of counting of said counting means.

15. Apparatus according to claim 9 whereinsaid synthesizing means includes phase-locked loop means responsive to said reference signal for generating a plurality of chopping waveforms and demodulator means operably connected to said phase locked loop means and responsive thereto and to said signal proportional to sin(wt-H9) for deriving therefrom signals proportional to sin0 and cost) for use in deriving said signals proportional to sin!) and sine/0.

16. Apparatus according to claim 15 wherein said chopping waveforms are 'rr/6 chopping waveforms.

17. Signal processing apparatus for deriving a digital representation of 0 from a signal proportional to sin(wt+6) and a reference signal including:

a. circuit means responsive to said signal proportional to sin(wt-i=6) andsaid reference signal for deriving therefrom signals proportional to sin6 and cosO;

b. synthesizing means operably connected to said circuit means and responsive thereto for deriving 11 l2 therefrom an output signal proportional to'sinO/Q; signal for integrating one of said signals in one direction for a time t and the other of said signals in c. summing means operably connected to said circuit the opposite direction for a time t until the output means and said synthesizing means and responsive of said integrating means returns to its original thereto for developing a composite signal propor- 5 state; and tional to sinfi and sinB/B; f. counting/processing means operably connected to d. switching means operably connected to said circuit said integrating means and responsive thereto for means and said synthesizing meand and adapted deriving therefrom a digital representation of 0. for selecting one of said signals proportional to sin6 18. Apparatus according to claim 17 wherein said and sin6/6; 0 synthesizing means includes means for incorporating a e. integrating means operably connected to said scale factor into said signal proportional to sin0/0 for switching means and said summing means and refacilitating conversion of 6 from radians to degrees. sponsive to said selected signal and said composite Patent No. 3, 39,716 Dated October 1, 197A George Reichnebacher It is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as 'shown below:

On the'I'itle page, in item 75 "Reiohnebacher'f should read v Reichenbacher Signed and sealed this 17th day of December 1974.

(SEAL)- Attest: v McCOY M. GIBSON JR. 0*. MARSHALL: DANN Attesting officer' Commissioner-of Patents FORM PO-OSO (\O-GSL v uscoMM-oc moan-P69 u;s. sovnmuzwr rnmnuo orncz: 8 93 UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 5, 39,716 Da e October 1, 197A Inventor(s) It is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:

On the Title page, in item 75 "Reichnebacher" should read Reichenbacher Signed and sealed this 17th day of December 1974.

I (SEAL)- Attest: McCOY M. GIBSON JR. cf. MARSHALLDANN Attesting Officer" Commissioner-of Patents FORM po-mso (!O-69)- v Y USCOMMDC and,

' v US. GOVIRNMEN? HUNTING OH'ICE: 9 

1. Signal processing apparatus for deriving a digital representation of theta from signals proportional to sin theta and cos theta including: a. synthesizing means responsive to said signals proportional to sin theta and cos theta for deriving therefrom a signal proportional to sin theta / theta ; b. integrating means operably connected to said synthesizing means and responsive to said signals proportional to sin theta and sin theta / theta for integrating one of said signals in one direction for a time t1 and the other of said signals in the opposite direction for a time t2 until the output of said integrating means returns to its original state; and c. counting/processing means operably connected to said integrating means and responsive thereto for deriving therefrom a digital representation of theta .
 2. Apparatus according to claim 1 wherein said signals proportional to sin theta and cos theta are derived from resolver-type signals proportional to sin theta sinwt and cos theta sinwt.
 3. Signal processing apparatus for deriving a digital representation of theta from signals proportional to sin theta and cos theta including: a. synthesizing means responsive to said signals proportional to sin theta and cos theta for derivinG therefrom an output signal proportional to sin theta / theta ; b. summing means operably connected to said synthesizing means and responsive to said signals proportional to sin theta and sin theta / theta for developing therefrom a composite signal proportional to sin theta and sin theta / theta ; c. switching means operably connected to said synthesizing means and responsive to said signals proportional to sin theta and sin theta / theta for selecting one of said signals; d. integrating means operably connected to said summing means and said switching means and responsive to said selected signal and said composite signal for integrating one of said signals in one direction for a time t1 and the other of said signals in the opposite direction for a time t2 until the output of said integrating means returns to its original state; and e. counting/processing means operably connected to said integrating means and responsive thereto for deriving therefrom a digital representation of theta .
 4. Signal processing apparatus for deriving a digital representation of theta from a signal proportional to sin(wt + theta ) and a reference signal including: a. synthesizing means responsive to said signal proportional to sin(wt + theta ) and said reference signal for deriving therefrom signals proportional to sin theta and sin theta / theta ; b. integrating means operably connected to said synthesizing means and responsive to said signals proportional to sin theta and sin theta / theta for integrating one of said signals in one direction for a time t1 and the other of said signals in the opposite direction for a time t2 until the output of said integrating means returns to its original state; and c. counting/processing means operably connected to said integrating means and responsive thereto for deriving therefrom a digital representation of theta .
 5. Apparatus according to claim 4 further including display means operably connected to said counting/processing means and responsive thereto for digitally displaying theta in degrees.
 6. Apparatus according to claim 4 wherein said synthesizing means includes means for deriving from said signal proportional to sin(wt+ theta ) signals proportional to sin theta and cos theta and means for synthesizing therefrom said signal proportional to sin theta / theta .
 7. Apparatus according to claim 6 wherein said means for synthesizing said signal proportional to sin theta / theta includes piecewise approximation means.
 8. Apparatus according to claim 4 wherein said synthesizing means includes means for incorporating a scale factor into at least one of said signals proportional to sin theta and sin theta / theta for facilitating the conversion of theta from radians to degrees.
 9. Signal processing apparatus for deriving a digital representation of a theta from a signal proportional to sin(wt+ theta ) and a reference signal including: a. synthesizing means responsive to said signal proportional to sin(wt+ theta ) and said reference signal for deriving therefrom signals proportional to sin theta and sin theta / theta ; b. integrating means operably connected to said synthesizing means and responsive thereto for integrating said signal proportional to sin theta in one direction for a time t1 and said signal proportional to sin theta / theta in the opposite direction for a time t2 until said integrating means returns to its original state; and c. counting means operably connected to said integrating means and responsive thereto for counting during said time period t2 to generate a digital representation directly proportional to theta .
 10. Apparatus according to claim 9 wherein said synthesizing means includes means for incorporating a scale factor into at least one of said signals proportional to sin theta and sin theta / theta for facilitating the conversion of theta from radians to degrees.
 11. Apparatus according to claim 9 wherein said synthesizing means incLudes means for deriving said signal proportional to sin theta / theta over an octant and further includes switching means for utilizing said signal proportional to sin theta / theta over all eight octants.
 12. Apparatus according to claim 11 wherein said synthesizing means includes segment sensing and switching means for deriving a piecewise approximation of said signal proportional to sin theta / theta over an octant.
 13. Apparatus according to claim 12 wherein said segment sensing and switching means effects said piecewise approximations of said signal proportional to sin theta / theta over three segments comprising an octant and wherein said segments comprise on the order of 23*, 12* and 10*.
 14. Apparatus according to claim 11 wherein said switching means includes octant sensing and switching means for presetting said counting means and for controlling the direction of counting of said counting means.
 15. Apparatus according to claim 9 wherein said synthesizing means includes phase-locked loop means responsive to said reference signal for generating a plurality of chopping waveforms and demodulator means operably connected to said phase locked loop means and responsive thereto and to said signal proportional to sin(wt+ theta ) for deriving therefrom signals proportional to sin theta and cos theta for use in deriving said signals proportional to sin theta and sin theta / theta .
 16. Apparatus according to claim 15 wherein said chopping waveforms are pi /6 chopping waveforms.
 17. Signal processing apparatus for deriving a digital representation of theta from a signal proportional to sin(wt+ theta ) and a reference signal including: a. circuit means responsive to said signal proportional to sin(wt+ theta ) and said reference signal for deriving therefrom signals proportional to sin theta and cos theta ; b. synthesizing means operably connected to said circuit means and responsive thereto for deriving therefrom an output signal proportional to sin theta / theta ; c. summing means operably connected to said circuit means and said synthesizing means and responsive thereto for developing a composite signal proportional to sin theta and sin theta / theta ; d. switching means operably connected to said circuit means and said synthesizing meand and adapted for selecting one of said signals proportional to sin theta and sin theta / theta ; e. integrating means operably connected to said switching means and said summing means and responsive to said selected signal and said composite signal for integrating one of said signals in one direction for a time t1 and the other of said signals in the opposite direction for a time t2 until the output of said integrating means returns to its original state; and f. counting/processing means operably connected to said integrating means and responsive thereto for deriving therefrom a digital representation of theta .
 18. Apparatus according to claim 17 wherein said synthesizing means includes means for incorporating a scale factor into said signal proportional to sin theta / theta for facilitating conversion of theta from radians to degrees. 